Question

I only need help with this one.

Can you also explain it for me and how I can solve future problems like this?

Answer 1

so hmm notice that template above, keep in mind that





`\bf \begin{array}{llll} \bullet \textit{ vertical shift by }{{ D}}\\ \qquad if\ {{ D}}\textit{ is negative, downwards}\\\\ \qquad if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}} \end{array}`

so hmm with that in mind, let's take a peek of yours


`\bf \begin{array}{llllll} g(x)=&(&x&-4)^2&+2\\\\ g(x)=&1(&1x&-4)^2&+2\\ &\uparrow &\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}`

C is -4, thus, the horizontal shift from f(x), is to the "right by 4 units", or you can use the C/B notation, will will be -4/1 or -4 anyway

Answer 2

horizontal
hmm

that means see only the left to right movement

ok, to move a function to the right c units, minus c from EVERY x
to move a function up c units, add c to the whole function


so we see the x terms
from x^2 to (x-4)^2+2
the +2 is irrelivant

4 was minused from every x
it was moved to the right 4 units


answer is 4


or you could do
vertex of f(x) is (0,0) and vertex of g(x) is (4,2) so from 0 to 4 is 4 to the right

answer is 4